Alexandra Daisy Ginsberg and the editors of Synthetic Aesthetics pulled no punches when they launched their new book at a “Friday late” at London’s Victoria and Albert Museum. A couple of audience members interrupted to bemoan the sheer abstractness of the enterprise. Why couldn’t the panel explain what synthetic biologists actually did? A rather unfair criticism of an event that scattered living biological materials across every floor of the museum. The task of explaining where beauty sits in the world of synthetic biology fell to Drew Endy, assistant professor of bioengineering at Stanford University, California. Endy explained how, when synthetic biology began, its self-styled “engineers” treated living things as wayward and overcomplicated machines, in need of radical simplification. Now, researchers are learning to appreciate and harness biological complexity. “Ford’s original Model T motor car was simple, in engineering terms, but it was hell to operate. A Tesla is complicated but a pleasure to drive.” Standards of beauty are fuzzy, personal and intuitive. They inspire real conversations. So I imagine talking about beauty in design is useful for a discipline that’s constantly struggling with its own hype, never mind other people’s panic.

In 1572, the civil engineer Rafael Bombelli published a book of algebra, which, he said, would enable a novice to master the subject. It became a classic of mathematical literature. Four centuries later, John Derbyshire has written another complete account. It is not, and does not try to be, a classic. Derbyshire’s task is harder than Bombelli’s. A lot has happened to algebra in the intervening years, and so our expectations of the author – and his expectations of his readers – cannot be quite as demanding. Nothing will be mastered by a casual reading of Unknown Quantity, but much will be glimpsed of this alien, counter-intuitive, yet extremely versatile technique.

Derbyshire is a virtuoso at simplifying mathematics; he is best known for Prime Obsession (2003), an account of the Riemann hypothesis that very nearly avoided mentioning calculus. But if Prime Obsession was written in the genre of mathematical micro-histories established by Simon Singh’s Fermat’s Last Theorem, Derbyshire’s new work is more ambitious, more rigorous and less cute.

It embraces a history as long as the written record and its stories stand or fall to the degree that they contribute to a picture of the discipline. Gone are Prime Obsession’s optional maths chapters; in Unknown Quantity, six “maths primers” preface key events in the narrative. The reader gains a sketchy understanding of an abstract territory, then reads about its discovery. This is ugly but effective, much like the book itself, whose overall tone is reminiscent of Melvyn Bragg’s Radio 4 programme In Our Time: rushed, likeable and impossibly ambitious.

A history of mathematicians as well as mathematics, Unknown Quantity, like all books of its kind, labours under the shadow of E T Bell, whose Men of Mathematics (1937) set a high bar for readability. How can one compete with a description of 19th-century expansions of Abel’s Theorem as “a Gothic cathedral smothered in Irish lace, Italian confetti and French pastry”?

If subsequent historians are not quite left to mopping-up operations, it often reads as though they are. In Unknown Quantity, you can almost feel the author’s frustration as he works counter to his writerly instinct (he is also a novelist), applying the latest thinking to his biography of the 19th-century algebraist Évariste Galois – and draining much colour from Bell’s original.

Derbyshire makes amends, however, with a few flourishes of his own. Also, he places himself in his own account – a cultured, sardonic, sometimes self-deprecating researcher. This is not a chatty book, thank goodness, but it does possess a winning personality.

Sometimes, personality is all there is. The history of algebra is one of stops and starts. Derbyshire declares that for 269 years (during the 13th, 14th and early 15th centuries) little happened. Algebra is the language of abstraction, an unnatural way of thinking: “The wonder, to borrow a trope from Dr Johnson, is not that it took us so long to learn how to do this stuff; the wonder is that we can do it at all.”

The reason for algebra’s complex notation is that, in Leibniz’s phrase, it “relieves the imagination”, allowing us to handle abstract concepts by manipulating symbols. The idea that it might be applicable to things other than numbers – such as sets, and propositions in logic – dawned with tantalising slowness. By far the greater part of Derbyshire’s book tells this tale: how mathematicians learned to let go of number, and trust the terrifying fecundity of their notation.

Then, as we enter the 20th century, and algebra’s union with geometry, something odd happens: the mathematics gets harder to do but easier to imagine. Maths, of the basic sort, is a lousy subject to learn. Advanced mathematics is rich enough to sustain metaphor, so it is in some ways simpler to grasp.

Derbyshire’s parting vision of contemporary algebra – conveyed through easy visual analogies, judged by its applicability to physics, realised in glib computer graphics – is almost a let-down. The epic is over. The branches of mathematics have so interpenetrated each other, it seems unlikely that algebra, as an independent discipline, will survive.

This is not a prospect Derbyshire savours, which lends his book a mordant note. This is more than an engaging history; it records an entire, perhaps endangered, way of thinking.

This is a book about the nature of the eye. It is about all the eyes that are, and ever have been, and may yet be. It is about how we see the world, and how other eyes see it. It is about what happens to the world when it is looked at, and about what happens to us when we look at each other. It is about evolution, chemistry, optics, colour, psychology, anthropology, and consciousness. It is about what we know, and it is also about how we came to know it. So this is also a book about personal ambition, folly, failure, confusion, and language.

On July 21, 1969 two astronauts set foot on the moon; far below, in ravaged Mozambique, a young revolutionary is murdered by a package bomb.

Strung like webs between these two unconnected events are three lives: Anthony Burden, a mathematical genius destroyed by the beauty of numbers; Saul Cogan, transformed from prankster idealist to trafficker in the poor and dispossessed; and Stacey Chavez, ex-teenage celebrity and mediocre performance artist, hungry for fame and starved of love. All are haunted by Nick Jinks, a man who sows disaster wherever he goes. As a grid of connections emerges between a dusty philosophical society in London and an African revolution, between international container shipping and celebrity-hosted exposés on the problems of the Third World, The Weight of Numbers sends the spectres of the baby boom’s liberal revolutions floating into the unreal estate of globalization and media overload—

The City is isolated. There is some land around the city, but beyond that there is nothing. Every twenty years the city performs the ceremony of the iron fish and things are changed. Years ago, whole sections of the city moved and were rearranged, new animals, new places arrived through the magic of the ceremony. But over time people have lost interest in it, and lost the rites and rituals to make the magic work.

Thomas Kemp grows up in the shadow of the ceremony and his father’s obsession with it. By the time the ceremony comes around again, he is one of the few who remembers or cares enough about it to begin preparations. ‘Simon Ings has created a strange world here, and one that has no explanation. Some of the inhabitants search for meaning, debate whether there is an outside world that their myths of jungles and oceans derive from. One of these is Kemp’s friend Blythe, an artist. Together they travel to find the edge of their world, and discover nothingness. Their journey changes them both in different ways. Blythe reacts to her experience by creating bleak and frightening work, while Kemp becomes an artist himself.

In a closed environment, what would happen to the people who live there? Their hopes and dreams, their need for freedom and new experiences? This is a place where all forms of artistic expression feed on each other and the past, constantly repeating and vainly striving.

I found this to be a deeply strange book, and I was impressed that the author did not try to explain the existence of the city, and the magic of the fish. Somehow it all worked better to read of Kemp’s life as he lived it, without knowing these things, and stumbling along in this strange world without a map. His passions, confusion, pain and everyday life are laid out to see, and even an evening’s drunken debauch has a ring of truth to it that is very appealing.’

I remember them. Their mouths, and their needles. That is all. That, and their painted eyes. Their mouths. They never spoke… So begins Adam’s odyssey into a nightmare of corruption and violence, where it is only his forlorn hope that he is helping his autistic son Justin that offers any solace. As everything implodes around him, Adam risks everything – his marriage, his family, his life – to lay hands on the one thing that might save him. His way out. His grail. A small bakelite box with a dial.

A grim, gripping and unrelenting tale in which a neat and happy ending is simply not an option. IRISH INDEPENDENT

Liz Jensen dropped into Arc’s offices to discuss her new book The Uninvited, an accessible and very frightening vision of ecological and political crisis.

“I thought about John Wyndham a lot,” she says, “and the ways he found to tell a complex, global story from a single, intimate point of view.” The result is chilling. Across the world, children are killing their families. The experts say it’s an isolated incident – and they’re wrong.

In June 2012 novelist Jake Arnott, best known for period thrillers The Long Firm and He Kills Coppers, talked to Arc about his novel The House of Rumour, an esoteric and sometimes disturbing reimagining of science fiction’s Golden Age.

Mike Harrison, whose story In Autotelia appeared in the inaugural issue of Arc, reveals his love of science, takes a wry view of the human project, and looks back on his ten-year effort to give science fiction its long-overdue Saturday night.

And here he discusses In Autotelia: “There’s more crammed into those 4000 words than there is crammed into the entire Light trilogy,” he says. “The fewer words you use, the more you can stuff in, which is why poetry is so good, and so hard to unpick.”